Spatial Statistical Properties of Pressure Solution Seams in Clastic Rocks in Southwest Ireland

Abstract

Length, height, thickness and spacing measurements of pressure solution seams at outcrop, hand sample and thin section scale were taken from clastic rocks located in the southwest of Ireland. The lengths and spacings of pressure solution seams have similarly shaped (approximately log-hyperbolic) distributions at the observed scales suggesting that length and spacing distributions are scale-independent over the scales studied with a fractal dimension in the range of 1.4 to 1.6. Pressure solution seam lengths and thicknesses are related by a power-law and their spacings have a linear relationship to bed thickness. Although pressure solution seams are often considered as anticracks (forming under the same remote stresses as joints, but with opposite sign) we describe how the mechanism of pressure solution differs substantially from that of jointing. We use an existing mechanical model to show that stresses around pressure solution seam tips are much lower than those for joints under equal but opposite loading conditions. Pressure solution seams also have a decreasing tendency to lengthen as they grow, which is reflected in their length distributions. We propose that pressure solution seams, unlike joints, do not reach fracture saturation spacing because of transverse coalescence.

Appendix: Configurations for Near-Tip Stress Distributions Associated with Pressure Solution Seams and Joints

To study the stresses at the tips of closing mode fractures and their possible reflections in the PSS statistics, we use the finite element mechanical model of Zhou and Aydin (2010). PSSs are idealized as elliptical local volume reduction structures (LVRSs) within a rock mass behaving in a linear elastic manner with Young’s modulus of 20 GPa and Poisson’s ratio of 0.25. An initial plastic volumetric strain of 20 % is set within the LVRSs which has the same elastic properties as the matrix. The remote compressive stress applied perpendicularly to the long axis of the LVRS is 100 MPa. The location at which the stress is calculated is at a distance, r, from the tip in the plane of the structure where r is 1.6 % of the half-length, $\frac{1}{2} L=a$ (Fig. 11). This distance is just outside of a potential process zone where high stresses are accommodated by processes that are not conceptualized as purely elastic (Willemse and Pollard 1998; Vermilye and Scholz 1998).

We use the analytical solution for opening mode crack near-tip stress intensity factor described by Lawn and Wilshaw (1975) to compare the tip stress magnitudes of joints to those of PSSs. To make comparisons to the closing mode model, the matrix surrounding the crack is assumed to have Young’s modulus of 20 GPa and Poisson’s ratio of 0.25 and the remote tensile stress of 100 MPa is applied perpendicularly to the long axis of the crack (Fig. 11) in order to compare it with that of the LVRS. Unlike in the closing mode case, the stress concentration result of the joint model is not dependent on its aspect ratio. The aperture/length ratio for joints in the literature is on the order of 1000 (Vermilye and Scholz 1995; Renshaw and Park 1997; Olson 2003; Schultz et al. 2008), which is one or two orders of magnitude higher than that of the PSSs measured in this study.

The stress distributions around the tip of an LVRS and an opening mode crack are also determined using the model described in Zhou and Aydin (2010). We model an LVRS with an aspect ratio of 100, consistent with our data, and an opening mode crack with an aspect ratio of 1000, which is consistent with published data and is comparable to that for the analytical solution for cracks. The opening mode crack is also modeled as an inclusion in the same way as an LVRS, but with Young’s modulus very close to zero (Fig. 13).